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Properties

Label 1332.2.q
Level $1332$
Weight $2$
Character orbit 1332.q
Rep. character $\chi_{1332}(529,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $1$
Sturm bound $456$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1332.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 333 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(456\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1332, [\chi])\).

Total New Old
Modular forms 468 76 392
Cusp forms 444 76 368
Eisenstein series 24 0 24

Trace form

\( 76 q - 2 q^{3} + q^{7} + 2 q^{9} + O(q^{10}) \) \( 76 q - 2 q^{3} + q^{7} + 2 q^{9} - 4 q^{11} + 3 q^{15} - 3 q^{21} - 6 q^{23} - 64 q^{25} - 23 q^{27} - 9 q^{29} + 6 q^{31} + 16 q^{33} - 18 q^{35} - 5 q^{37} - 12 q^{39} + 12 q^{41} + 6 q^{43} + 3 q^{45} - 2 q^{47} - 39 q^{49} - 18 q^{51} + 14 q^{53} + 42 q^{57} + 3 q^{59} + 37 q^{63} + 32 q^{65} - 20 q^{67} - 3 q^{69} - 13 q^{71} - 14 q^{73} + 3 q^{75} + 36 q^{77} - 3 q^{79} + 14 q^{81} - 34 q^{83} - 12 q^{85} - 6 q^{87} - 30 q^{89} - 21 q^{91} + 6 q^{93} + 22 q^{95} - 48 q^{97} + 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1332, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1332.2.q.a 1332.q 333.k $76$ $10.636$ None 1332.2.q.a \(0\) \(-2\) \(0\) \(1\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1332, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 2}\)